In many languages different communities speak in a different way. However about languages like Russian one likes to assert that all people speak the same way. How does this work in Esperanto?
I think it is human nature that if you meet with the same group of people often enough you end up creating your own set of words and phrases that might not be understood outside of your circle, and Esperanto is no exception to this. For example, in the London youth group it is very common to use the word pabo to refer to a British-style pub. There is also a tendance to use words like maljam, malpo, na and even givupi. This works because if you know the people you are talking to well you also know what kind of words they're likely to understand. I think this doesn't really damage the comprehensibility of Esperanto because of course people using these words are also able to communicate using a more “standard” Esperanto with people they don't know as well.
In the Ĉu… books by Johán Valano there is a fictional dialect of Esperanto. All of the stories take place in an un-named fictional country where Esperanto is the national language. The main protagonists live in a region called Sanktavalo which has its own dialect and Johán Valano describes in detail the particularities of this dialect. For example they use an infinitive after the preposition pro:
“Li estas arestita, ĉu ne? Pro kio? Pro ŝmire skribi sur la Granda Ponto?”
They also use prepositions as adverbs and elide the initial ‘e’ in estas.
“Cetere, li stas sekretema. Li rajtas, ĉu ne? Se li ne volas konfidi, mi respektu lian deziron. Diru al mi! Ĉu vi scias ion prie?”
Dialects come about because of geographical separation of various groups of speakers of the same language. Of course, Esperanto speakers are very much geographically separated, but the way it is used in practice hinders the appearance of dialects: People use it a lot to communicate with people who live far away, so that linguistic innovation spread without much geographical restrictions.
Additionally, there is at any rate very little evolution in Esperanto besides new words for new concepts, because many Esperanto speakers try to stick to what is already considered standard, so as to make themselves understood better, and so as to contribute to the stability of the language.
Of course, one can observe differences in usage based on the native language of the Esperanto speaker. But this is a different phenomenon from a dialect. People generally try to get rid of the influence of their native language when they improve their Esperanto. And those Esperanto speakers that are considered most proficient in the language hardly exhibit any features of their native language in their Esperanto.
So dialectical variation in the normal sense of the term does not exist in Esperanto.
Esperanto was created to have one common language that is easy to learn with as much in common as possible and as little variation as possible. That doesn't mean that people haven't enriched the language or wanted to change it in different ways. Let's go to a dictionary definition of dialect: "a variety of a language that is a characteristic of a particular group of the language's speakers". The differences can be in vocabulary, grammar as well as pronunciation. Wikipedia: Dialect
A dialect doesn't necessarily have to be because of geographical reasons, it could be a sociolect - distinguished by social class or ethnicity. What about la mava lingvo? Could neologism-heavy [nezamenhofa, nefundamenta] language be viewed as a sociolect? Toño del Barrio argues that this is a different register of the language. What about people that use iĉismo? Are they using a different sociolect of Esperanto? If we say "this is not official Esperanto", does that make it the iĉisma dialect?
There certainly are slang words and different word order used across all Esperantujo, but is it codified enough to call it a dialect? I hardly have enough experience to tell. It certainly is worth it not to forget that dialects aren't necessarily only due to geographical divides.
I'd also like to add that Esperanto native speakers have been noted to have grammatical differences, such as using compound tenses and the accusative case, as well as more flexibility with grammar and words that an Esperantist who learned the language later in life might not otherwise use (i.e, "evening" would be malmateno instead of vespero, "nothing" would be malio instead of nenio, "to bathe" would be kuvi instead of bani sin, etc).
I think this could be considered a native accent/dialect in Esperanto (as in both natives and fluent non-natives may speak it without errors but use the language in different ways).
Not really, since the goal of Esperanto is to avoid such problems. The most notable difference between different Esperanto communities is probably sentence structure - English-speaking Esperantists usually prefer the subject-verb-object structure, such as "Mi manĝis la manĝaĵon," but speakers of languages that don't have a SVO structure often don't structure their sentences that way (this is why the accusative is important).
There are regional preferences on synonyms.
plaĝo = strando (= beach)
It will come to no surprise that French influenced speakers tend to plaĝo and German ones to strando.
There is formal (estas ~inta) and informal usage (~is), youth jargon and so on that is influenced by the location of the Esperanto community.
However there are hardly dialects overall - one experiences. More distighuishing are accents, the progress of local groups and speakers.
Even historic Esperanto does not seem that outdated as old German or English.
There is an Esperantido called Popido constructed to act as a dialectal form of Esperanto. It is sometimes used in Esperanto literature, e.g., in Deck Dorval, Kazinksi venas tro malfrue.
I could see there being different dialects in terms of using plaĝo vs strando etc; but also word order, which isn't really a big deal. The real issue could be what @Kasenjo said about denaskuloj using malmateno instead of vespero. Vespermanĝo would be malmatenmanĝo. I don't think a word like that would be so difficult to figure out, but malio instead of nenio could be more difficult to figure out that it's mal+io, but that may be a problem for some & not others. That could turn into a dialect that isn't entirely intelligible on both sides.